I am literally a professional pedant and 'another thing coming' being absolutely correct is a hill I am prepared to figuratively die on.
The 'another thing' could quite simply be another thought, another fact, another opinion, another factor. It's a wider, more general noun than 'think' and makes perfect sense to me, let alone it's what we all say round here.
'Think' implies an active effort by the thinker/wrong person. 'Thing' is more passive, meaning it will happen regardless of the thoughts of the thinker/wrong person. In this sense, it is quite often used as some kind of veiled threat.
In my professional pedantry, I have to consider what most people say and will understand. There is quite often no 'wrong' in English, only style, register, common parlance and comprehensibility. If most people understand 'having another thing coming' to mean something along the lines of 'you're wrong [because of X]', then its usage is totally admissible.
Incidentally, 'easier for a camel to pass through the eye of a needle' is only one letter away from 'easier for a rope to pass through the eye of a needle' in the primary Greek (those pesky translators). So although the latter version would make more sense, it is the former that is 'correct'. These things are often strange, convoluted and arbitrary, so the idea of one thing, and one thing only, being 'correct' is something that should be treated with care and caution.